Interacting Topological Crystalline Insulators

Hiroki Isobe, Liang Fu

Titus Neupert, Frank Schindler

Upendra Kumar

Liujun Zou

Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected by crystalline (and other) symmetries. They are originally predicted by band theories, so an important question is their stability under interactions. In this paper, by directly studying the physical bulk properties of several band-theory-based nontrivial TCIs that are conceptually interesting and/or experimentally feasible, we show they are stable under interactions. These TCIs include (1) a weak topological insulator, (2) a TCI with a mirror symmetry and its time-reversal symmetric generalizations, (3) a doubled topological insulator with a mirror symmetry, and (4) two TCIs with symmetry-enforced-gapless surfaces. We describe two complementary methods that allow us to determine the properties of the magnetic monopoles obtained by coupling these TCIs to a U(1) gauge field. These methods involve studying different types of surface states of these TCIs. Applying these methods to our examples, we find all of them have nontrivial monopoles, which proves their stability under interactions. Furthermore, we discuss two levels of relations between these TCIs and symmetry enriched U(1) quantum spin liquids (QSLs). First, these TCIs are directly related to U(1) QSLs with crystalline symmetries. Second, there is an interesting correspondence between U(1) QSLs with crystalline symmetries and U(1) QSLs with internal symmetries. In particular, the TCIs with symmetry-enforced-gapless surfaces are related to the “fractional topological paramagnets” introduced in Zou et al. [arXiv:1710.00743].

Stephan Rachel, Karyn Le Hur

Liujun Zou

The notion of symmetry protected distinctions among quantum phases has been well appreciated in understanding many-body systems. As a prominent example, recent studies on topological crystalline insulators (TCIs) indicate that these insulators are nontrivial if and only if the relevant crystalline (and some other) symmetries are preserved. By bulk-boundary correspondence, the authors study the properties of the bulk magnetic monopoles of some TCIs that are conceptually interesting and/or experimentally feasible, and argue that this bulk characterization is a more direct and unified physical description of a TCI. In doing so, the authors prove the stability of these TCIs with respect to interactions.